Conclusions In the present chapter, the advantages and limitations have been considered of deconvolution techniques for improving the accuracy and resolution of the remote sensing of at
Trang 1case, the “empirical” statistical error is estimated by simulations with respect to the temperature profile obtained from the convolved, long-pulse lidar profiles in absence of noise The same as the above-described is the behavior of the restored profiles in the case of
lower electron concentration ne = 2x1019 m-3 Because of the lower SNR in this case, the
quality of the restored profiles is somewhat lower compared to the case of ne=9x1019 m-3
0
1
2
3
4
5
0.0 0.1 0.2 0.3 0.4
Model Restored
(a)
Radius [m]
Theoretical error
Numerical error
0 1 2 3 4 5 6 7
0.0 0.5 1.0 1.5 2.0
Model Restored
(b)
Radius [m]
Theoretical error Numerical error
0
1
2
3
4
5
6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.7
Restored
Radius [m]
Theoretical error Numerical error
0 1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.7
Restored
Radius [m]
Theoretical error Numerical error
Fig 13 Electron temperature profiles restored on the basis of the convolved (a) and
deconvolved lidar profiles without filtering (b), and on the basis of the deconvolved lidar
profiles smoothed by a monotone sharp-cutoff digital filter (with W=3ct0/2) (c) and by a moving average filter (with W=2ct0/2) (d); the right-hand y axis represents the
theoretically estimated relative rms errors compared to the numerically obtained ones; ne =
9x1019 m-3
The results of applying the deconvolution approach in the case of increased sensing pulse
energy (E0=3 J) are shown in Fig.14, where it is seen that the restoration accuracy is higher
due to the higher SNR This allows one to detect reliably smaller-scale inhomogeneities of the finer structure of the electron temperature profiles In general, the increase of SNR, due for instance to increasing the electron concentration, the sensing pulse energy or the sensitivity of the photodetectors, is determinant for achieving high retrieval accuracy and resolution
Trang 22.0 2.5 3.0 3.5 4.0
0
1
2
3
4
5
Restored
Radius [m]
0 1 2 3 4 5
Restored
Radius [m]
0 1 2 3 4 5
Restored
Radius [m]
Fig 14 Electron temperature profiles restored on the basis of the convolved (a) and
deconvolved lidar profiles smoothed by a monotone sharp-cutoff digital filter (with
W=3ct0/2) (b) and by a moving average filter (with W=2ct0/2) (c); ne=9x1019 m-3, E0= 3 J
The statistical error represented by error bars, (b) and (c), is estimated on the basis of Eq.(54)
5 Conclusions
In the present chapter, the advantages and limitations have been considered of deconvolution techniques for improving the accuracy and resolution of the remote sensing
of atmosphere, thermonuclear plasmas, and other objects by lidars of relatively long pulse response function including the laser pulse shape Analog and photon counting modes of direct signal detection have been concerned The general Fourier and Volterra deconvolution algorithms have been analyzed as well as some simple and fast special algorithms for the cases of rectangular, rectangular-like and exponentially-shaped pulse response functions At negligible noise level, a high accuracy of recovering the short-pulse lidar profile is achievable at sufficiently short computing step Also, by using suitable approaches, in some cases one can reduce the characteristic retrieval distortions due to some pulse response uncertainties The strong broadband noise effect on the retrieval accuracy and resolution is revealed, including the noise accumulation with the distance of sensing for the recurrence algorithms The noise influence in this case is shown to be effectively reduced by using appropriate compromise filtering or choice of the computing
Trang 3step That is, to avoid retrieval distortions, the filter window or the computing step should exceed the noise correlation radius (or time) but be less than the least variation (spatial or temporal) scale of the short-pulse lidar profile The deconvolution procedures are shown as well to decrease the disturbing effect of narrow-band noise whose correlation time exceeds the pulse duration Let us also underline the fact that the deconvolution-based retrieval of the short-pulse lidar profiles allows high-resolution sensing of small finite-size objects by longer laser pulses, realizing in this way double-sided linear-strategy optical tomography of such objects
The investigations performed show as well that Fourier-deconvolution procedures, combined with appropriate low-pass filtering, applied to the measured Thomson scattering lidar profiles lead to several (2-3) times better resolution of recovering electron temperature profiles in fusion plasma, under conditions of plasma light background and amplification-enhanced Poisson noise The convolution-due systematic errors are essentially corrected for and an acceptable restoration accuracy is achieved allowing one to reveal characteristic inhomogeneities in the distribution of the electron temperature within the plasma torus It is also shown that, naturally, because of higher signal-to-noise ratio (stronger lidar return) the deconvolution accuracy increases with the increase of the electron concentration and the sensing pulse energy This means that the deconvolution approach would be especially appropriate for processing data from a new generation of fusion reactors, such as ITER and DEMO, characterized by considerably higher electron concentration and sensing pulse energy compared to these achievable in JET
6 Acknowledgments
This results described in the chapter was funded partly by the Bulgarian National Science Fund under Projects Ph-447, Ph-1511, and DO 02-107/2009 and the European Communities under the Contract of Association between EURATOM and INRNE (Bulgaria) This work was carried out in part within the framework of the European Fusion Development Agreement The views and opinions expressed herein do not necessarily reflect those of the European Commission
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